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Probability Seminar Spring 2008

Time: Wednesdays, 11-12
Place: Braunstein 326
  1. April 5-6 AMS Meeting #1038, Bloomington
  2. April 9: no seminar
  3. April 10, 4-5: Florence Merlevède, Université Paris 6 Rates of Convergence in the Central Limit Theorem
    This talk will survey some distances between two probability laws and the relations between them. They are used to obtain various rates of convergence in the central limit theorem for sums of independent and dependent random variables.
  4. April 16: no seminar
  5. April 23: no seminar
  6. April 30: Magda Peligrad Ibragimov's conjecture
  7. May 7: Sunder Sethuraman (Iowa State U) Martingale proof of Dobrushin's CLT.
  8. May 14: Wlodek Bryc, Random Toeplitz and other structured matrices>.
  9. May 21: Arup Bose (Indian Statist. Inst.), Limiting Spectral Distribution of Random Matrices.

Probability Seminar Winter 2008

Time: Wednesdays, 1-2
Place: Old chem 804
  1. Jan 24, Th 4-5: Todd Kemp (MIT), Colloquium Talk: Logarithmic Sobolev inequalities: new insights on an important tool
    The logarithmic Sobolev inequality, discovered by L. Gross, is a weak form of a Sobolev inequality: it gives control of a function through average information about its derivatives. It has become a ubiquitous tool in global analysis and probability theory, with important applications in stochastic analysis, large deviations, spectral theory, non-linear PDE, geometric analysis, non-commutative geometry, and more. As a stunning example, the logarithmic Sobolev inequality inspired Perelman's proof of the Poincar\'e conjecture.

    In this talk, I will give an introduction to the area of logarithmic Sobolev inequalities. I will then discuss new insights on such inequalities in the context of regular function spaces, such as holomorphic and subharmonic functions. In recent work with P. Graczyk, J. Loeb, and T. Zak, we have discovered a new and very general logarithmic Sobolev inequality for logarithmically-subharmonic functions. I will discuss these results and give clues about their significance.

  2. Jan 25, Fri, 1-2 Old Chem Room 807: Special Seminar, joint with Geometric Analysis. Speaker: Todd Kemp (MIT), Logarithmic Sobolev inequalities: new insights on an important tool
  3. Jan 30: no seminar
  4. Feb 6: Sunder Sethuraman (Iowa State U): On a locker problem
  5. Feb 13: Wlodek Bryc Wick formula for quaternion-valued Gaussian n-touples. (based on joint work in progress with Virgil Pierce) Notes
  6. Feb 20: Magda Peligrad Exponential martingale approximation for linear process
  7. Feb 27: no seminar
  8. March 5: M. Bhaskara Rao The Krein-Milman Theorem -- a puzzler
  9. March 12: M. Bhaskara Rao (continued)
Spring break: March 24-29

Probability Seminar Autumn 2007

Time: Wednesdays 3-4
Place: Chem 605
  1. Oct 3: no seminar (RPT)
  2. Oct 10: Jeesen Chen, On the probability of a lucky number
  3. Oct 17: Rec center 3210 Tamer Oraby, PhD defense
  4. Oct 24: no seminar
  5. Oct 31: no seminar
  6. Nov 7: no seminar
  7. Nov 14: no seminar
    • Thursday, Nov 15 Colloquium talk by Virgil Pierce, OSU. Recent Results for the Toda and Pfaff Lattice Hierarchies Abstract: Orthogonal and unitary ensembles of random matrices are standard models for statistical and quantum physics. A fundamental object of study is the partition function, which is expressed as an integral over the ensemble of matrices. In the unitary case this function is a tau-function of the Toda lattice hierarchy, meaning it generates solutions of the hierarchy. The Toda lattice is a classical example of an integrable hierarchy and possesses a number of interesting structures. In the orthogonal ensemble case, Adler and van Moerbeke showed that the partition function is a tau-function of the Pfaff lattice hierarchy. Yuji Kodama and I have shown that the Pfaff lattice is an integrable system. I will outline the above relations, show how they are useful for finding explicit solutions of some graphical combinatoric problems and illustrate some recent results for the Pfaff lattices.
  8. Nov 21: no seminar
  9. Nov 28: ~

Stochastic Calculus study group

organized by B. Zhang and T. Oraby will study An Introduction to Stochastic Differential Equations (version 1.2) by L. C. Evans.

Tuesdays 5-7 in the math launge

  • Ch 2, Probability: Tamer (2 weeks)
  • Ch 3, Brownian motion, Hongjun Wang (2 weeks)
  • Ch 4, Stochastic integrals, ... (2 weeks ?)
  • Ch 5, Stochastic diff eqtns ... (2 weeks ?)
  • Ch 6, Applications
... (N-1 weeks)

Probability Seminar Spring 2007

Time: Mondays 2-3
Place: Seminar Room Chem 807
  1. Th, March 28, 4-5 in Braunstein 309, Michael Woodruff (University of Michigan), The Law of the Iterate Logarithm for Stationary Processes
    Abstract: The Law of Large Numbers, the Central Limit Theorem, and the Law of the Iterated Logarithm for independent and identically distributed sequences of random variables are three central, perhaps dominant, results of classical probability theory. The Ergodic Theorem provides a complete extension of the Law of Large Numbers to sequences that are dependent, but stationary. The Central Limit Theorem and Law of the Iterated Logarithm do not extend as completely, but only under additional conditions that effectively limit the amount of dependence. During the past decade there has been some progress on understanding the Central Limit Theorem for stationary processes, resulting in conditions that are sufficient and nearly necessary, at least for the conditional version of the Central Limit Theorem. The talk will present recent efforts to modify the arguments leading to the Central Limit Theorem to obtain a Law of the Iterated Logarithm. It will begin with some background material on the Law of the Iterated Logarithm and a selective review of recent work on the Central Limit Theorem for stationary sequences. It will then describe the modifications necessary to obtain the Law of the Iterated Logarithm.
  2. April 9: no seminar
  3. April 16: no seminar
  4. April 23: Florence Merlevède, Université Paris 6 Rates of convergence for the Wasserstein distances in the central limit theorem for stationary sequences
    Abstract: In this joint work with J. Dedecker and E. Rio, we obtain convergence rates in the central limit theorem for stationary sequences in Lp for Wasserstein distances of order r, for p in ]2,3] and r in ]p-2,p]. The conditions are expressed in terms of projective criteria. The results apply in particular to non-adapted sequences.
  5. Colloquium talk: Thursday, April 26: Wlodek Bryc Classical and noncommutative probability
  6. April 30: M. Bhaskara Rao Patterns in coin tossing
  7. Colloquium on Tue, May 1 at 4PM Sunder Sethuraman Iowa State University On Scaling Limits of a Tagged Particle in Simple Exclusion Particle Systems
    Informally, the simple exclusion process follows a collection of random walks which interact in that they are not allowed to jump onto each other. In this talk, we consider the motion of a distinguished, or tagged, particle in this particle system. We review some of the past results and discuss some new contributions.
  8. May 7: Wlodek Bryc, Moments of real Wishart matrices
  9. May 14:
  10. May 21:
  11. May 28: no seminar (holiday)

Probability Seminar Winter 2007

Time: Mondays 2-3
Place: Seminar room Chem 807
  1. Jan 22: Magda Peligrad, Moderate deviation under projective criteria
  2. Jan 29: Sunder Sethuraman, On the count of certain strings in Bernoulli sequences
  3. Feb 5: Wlodek Bryc Asymptotic normality of traces of polynomials in Wishart matrices
  4. Feb 12: canceled
  5. Feb 19: Tamer Oraby On Shoshnikov's approach to maximal eigenvalue problem
  6. Feb 26: Special Room Swift 620 Tamer Oraby, Practice interview talk.
  7. March 5: Magda Peligrad Processes with negatively associated increments
  8. Thursday, March 15. Time: 4PM Place: Braunstein 309: Roland Speicher, Queens Strong Haagerup inequalities
    In a holomorphic context, some analytic inequalities improve when restricted to a holomorphic subalgebra. We are exploiting this phenomena in a non-commutative situation. Concretely, we show that one can improve Haagerup's classical inequality for norms of convolution operators on the free group if one restricts to operators which involve only the generators (but not their inverses) of the free group. The proof relies on a good understanding of moments of the involved operators and is mainly combinatorial. This is joint work with Todd Kemp.
  9. March 16/17: AMS meeting Miami University, Oxford, OH.

Functional Analysis Seminar

Wednesday 3-4 pm, Feb 21, Feb 28, March 7 Seminar room (OC 807) Victor Kaftal, Majorization theory for infinite sequences
Majorization for finite sequences is linked to doubly stochastic matrices, convexity, the diagonals of selfadjoint matrices (the Schur-Horn Theorem) and more, and so it has been of interest to researchers in several areas of math. Little was know until recently about majorization for infinite sequences but we have now some new results.

Probability Seminar Autumn 2006

Time: Mondays 2-3
Place:Chem 807
  1. Sept 25: Organizational meeting
  2. Oct 2: Wlodek Bryc Complex Wishart matrices
  3. Oct 9: Wlodek Bryc Complex Wishart matrices, continued
  4. Oct 16: Sunder Sethuraman (Iowa State U) On some random graph problems
  5. Oct 19: 4-5 PM Colloquium talk: Dalibor Volny University of Rouen, France

    Martingale approximation of stationary sequences

    In the last few years, important contributions to the study of martingale approximations of stationary processes have been published. I'll have a closer look at the Wu and Woodroofe approximation (Ann. Probab. 2004) and I shall indicate that it can be generalized to non adapted processes. The method easily extends to the CLT of Maxwell and Woodroofe (2004) but not to the invariance principle of Peligrad and Utev (2005); there the non adapted version seems to remain open. Various examples will show that the martingale approximation depends on the choice of the filtration.
  6. Oct 21-22: AMS meeting
  7. Oct 23: no seminar
  8. Oct 30: Magda Peligrad, Inequalities and limit theorems under weak association.
  9. Nov 6: Magda Peligrad, Inequalities and limit theorems under weak association (cont.)
  10. Nov 13: no seminar(?)
  11. Nov 20: Room: Swift 608 Time: 2-3 Pando Georgiev (CS Dept) Independent Component Analysis and a cross-cumulant measure for independence
    We revisit some cumulant methods for Independent Component Analysis - an unsupervised learning method with increasing popularity and applicability in number of disciplines. A rigorous justification of identifiability of the linear ICA method by kurtosis maximization is given by a simple lemma from optimization theory, which gives a basis for a generalization of the famous Fixed Point Algorithm for ICA for high order cumulants. We propose a measure for independence of group of random variables, given by a sum of cross-cumulants of a given order n. Similar measure was known for the case of four order cross-cumulants from the JADE algorithm for ICA. We derive a formula for its calculation using cumulant tensors. In the case n=4 our formula allows efficient calculation of this measure, using cumulant matrices. Much attention is devoted to the case of six order cross-cumulants, aiming to show that this measure can be calculated using again cumulant matrices. We provide a simple proof of the main ICA theorem concerning identifiability of the linear ICA model using the properties of the cross-cumulants instead of the Darmois-Skitovitch theorem from statistics, used for this purpose in the literature on ICA. Various ICA algorithms are demonstrated.
  12. Nov 27: M. Bhaskara Rao A discrete probability problem in chemical bonding

Probability Seminar Spring 2006

Time: Mondays, 11-12
Place: Seminar Room
  1. Apr 3:
    • Organizational meeting
    • Wlodek Bryc: Natural Exponential Families and their free counterpart (Based on joint work with M. Ismail) |Slides|(.4MB)
  2. Apr 10: Magda Peligrad Moderate Deviations
  3. Thu, Apr 13, 4-5PM: Colloquium Talk by Florence Merlevède, Université Paris 6 On the weak invariance principle for non-adapted sequences under projective criteria
    I shall present some results about the central limit theorem and its weak invariance principle for sums of non-adapted stationary sequences, under different normalizations. Our conditions involve the conditional expectation of the variables with respect to the given sigma-algebra, as done in Gordin (1969) and Heyde (1974.) These conditions are well-adapted to a large variety of examples, including linear processes with dependent innovations or regular functions of linear processes.
  4. Apr 17: Tamer Oraby, Free multiplicative convolution
  5. Thu, Apr 20, 4-5PM: Colloquium Talk by Sunder Sethuraman, Iowa State University Diffusivity of a tagged particle in a "zero-range" system of interacting particles
    The "zero-range" system is an (infinite) collection of dependent random walks on Zd which models various types of traffic. Informally, the interaction is in that a particle jumps with a rate depending on the number of particles at its vertex, but to where it jumps is selected independently. In this talk, we consider a distinguished, or "tagged," particle in this system and discuss its asymptotic behavior including some recent diffusive estimates in "equilibrium." In particular cases, we also discuss approximation of the tagged position by a Brownian motion with parameters depending on the form of the interaction and the density of particles.
  6. Apr 24 Room Change:Rec Center 3230: Krzysztof Podgorski, IUPUI, Genomics, microarray analysis and mathematical statistics
  7. May 1 Room Change:Rec Center 3230: M. Bhaskara Rao, One Bulb? Two Bulbs? How many bulbs light up? A problem from a pharmaceutical company
  8. May 8: Wlodek Bryc Quadratic Harnesses
    This is a "practice talk for a conference". The topic is classificiatioon of rpocesses with linear regressions and quadratic conditional variances.
  9. May 15 Room Change:Rec Center 3230: Wojciech Matysiak Random sequences with linear regressions - an operator approach
  10. May 22: Room Change:Rec Center 3230 Tamer Oraby Limiting spectra of random block matrices
  11. May 29: (Memorial Day - no classes)

Probability Seminar Winter 2006

Time: Mondays, 3-4, 4-5
Place: Chem 724

Schedule

  1. Jan 9: no seminar
  2. Jan 16: holiday
  3. Jan 23: Tamer Oraby, The limiting spectra of Girko’s block-matrix
  4. Jan 30: ?
  5. Feb 6: (none)
  6. Feb 13: (none)
  7. Feb 20: posponed?
  8. Feb 27: Magda Peligrad Moderate deviations for martingales
  9. March 6:
  10. March

Related Activities

  1. 6H Mini Course Introduction to Large Deviations (W. Bryc)
    • Tue, Jan 3, 3:30-5:30, Introduction
    • Th, Jan 5, 3:30-5:30, Equivalent Definition, Criteria
    • Th, Jan 12, 3:30-5:30, Ben Arous-Guionnett's Theorem
  2. Feb 4-18: visit by R. Szwarc

Statistics Seminar

Wednesdays 3-4, Room 825

Probability Seminar Fall 2005/06

Schedule

  1. Sept 28: Organizational meeting in Seminar Room
  2. October 5: Tamer Oraby, Limiting spectral distribution of symmetric matrices with weakly dependent entires
  3. October 12: Mourad E.H. Ismail,University of Central Florida Orthogonal Polynomials and Birth and Death Processes
    Abstract We survey the role played by orthogonal polynomials in the analysis of transision probabilities of birth and death processes and associated random walks. Several examples will be mentioned.
    • Th, October 13, 4PM: colloquium Talk Mourad E.H. Ismail,University of Central Florida Orthogonal Polynomial, Discriminants, and Electrostatic Equilibrium Problems
      Abstract Stieltjes and Hilbert computed discriminants of Jacobi polynomials. Stieltjes studied the electrostatics equilibrium problem of n-unit charged particles restricted to (-1,1) under the external field of charges (a+1)/2 and (b+1)/2 at ±1. The potential is a logarithmic potential. Stieljes showed that the equilibrium position of the particle is at the zeros of the Jacobi polynomial Pn(a, b)(x). We discuss the recent developments on this problem, its extension to general orthogonal polynomials and the role discriminants play in the solution of the problem. We also mention the more recent work where similar techniques are used to solve the Bethe Ansatz equations for the XXZ and XXX models.
  4. October 19: Magda Peligrad Asymptotic negative association
  5. October 21: Twenty-Seventh Midwest Probability Colloquium October 21-22, 2005 http://www.math.northwestern.edu/mwp/
  6. October 26: Wlodek Bryc, Some open questions on random matrices Slides(300KB)
  7. Nov 2 Computer Lab: Arup Bose, Indian Statistical Institute Limiting Spectral distribution of random matrices
  8. Nov 9: Wlodek Bryc Exponential Families
  9. Nov 16: Zeynep Teymuroglu Optimal Portfolio Theory
    Abstract We assume that real-world financial markets are partially hedgable, therefore they are fundamentally incomplete [3]. It has been known for some time that there is no unique price for financial contracts in incomplete market. Recently, by the help of reduced Monge-Ampere equations, [1] introduces a new method for pricing and hedging of financial instruments in in/complete market. Financial contracts still have non-unique prices in incomplete setting, but the prices depend on only g, so-called relative risk aversion.
    • [1] S.D. Stojanovic: Higher dimensional fair option pricing and hedging under Hara and Cara utilities. (Preprint, August 2005)
    • [2] S.D. Stojanovic: Pde methods in financial modeling. 25th Annual Searcde in Dayton
    • [3] S.D. Stojanovic: Actuaries vs. Financial Engineers in regard to valuation: the truth is now found to be in between. Garp Risk Review, Sept/Oct 2005
  10. November 18, 2-3:15 pm, 1216 Crosley Tower: Arup Bose, Indian Statistical Institute, TBA Dept Economics Seminar
  11. Nov 23: seminar cancelled
  12. Nov 30: Wojtek Matysiak Random sequences with linear regressions

Probability Seminar Summer 2005

Probability Seminar Spring 2005

Probability Seminar Winter 2005

Probability Seminar Fall 2004

Time: Mondays 2-3.

Probability Seminar 2004 (Summer)

Summer visitors

Probability Seminar 2004 (Spring)

Schedule

  • March 29: Wlodek Bryc: Biane's proof of Borovkov-Utev's Theorem. Based on P. Biane, Logarithmic Sobolev inequalitites, matrix models and free entropy, Acta Math. Sinica. Vol 19, No3, (2003), 1-11
  • April 5: Jeesen Chen, Unsmoothing inequality
  • April 12: Jeesen Chen Unsmoothing inequality (continued)
  • April 19: Magda Peligrad, Maximal inequalities for martingale-like sequences (continued)
  • April 26: none
  • May 3: Wlodek Bryc Spectral measure of large random Hankel , Markov , and Toeplitz matrices
  • May 10: Cancelled
  • May 17: Wlodek Bryc Harnesses, polynomial martingales, free Levy processes
  • May 24: Jeesen Chen Covariance kernell and its applications
  • Colloquium May 27 (Th): Rick Bradley (Indiana University), Pairwise independence, triple-wise independence, and the central limit theorem
  • Special Probab Seminar May 28 (Friday!) 4-5PM in Seminar Room 807: Rick Bradley (Indiana University), On a stationary, triple-wise independent, absolutely regular counterexample to the central limit theorem
    This seminar talk will treat in more detail the topic of the Colloquium talk. It will focus on two particular examples of strictly stationary, triple-wise independent random sequences for which the central limit theorem fails. One of the examples has two states and is ergodic. The other has three states and satisfies a stronger condition known as absolute regularity.
  • May 31: no seminar (Memorial Day)
  • Colloquium June 3 (Th) Florence Merlevède (Univ. Paris VI), Limit Theorems and Deviation Probability of Cramer-von Mises Statistics Drawn from Dependent Random Variables

FA Seminar We 2-3 Room 708

    • April 14: Bogdan Vishnesku Free probability
    • April 21: Bogdan Vishnesku Free probability (cont)
    • April 28: Bogdan Vishnesku Free probability (cont)
    • May 5: Bogdan Vishnesku Free probability (cont)
    • May 12: Bogdan Vishnesku Free probability (cont)
    • May 19: Bogdan Vishnesku Free probability (cont)
    • May 26: Bogdan Vishnesku Free probability (cont)

Probability Seminar 2004 (Winter)

Probability Seminar 2003 (Autumn)

Probability Seminar 2002 (Winter)

Probability Seminar 2001 (Winter)

Probability Seminar 2000